More Examples of Direct Proof

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In this video, we present some more examples of direct proof. This time, instead of writing the proof in real time, we read already finished proofs and discuss their structure.

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Awesome video & explanation for us at the lower level maths Dr. Misseldine. Question for you that other low level students may ask: why not justify each line as in geometry proofs and so on? I ask this mainly because when we actually SHOW our work or offer a justification we may be able to see mistakes in our work. That is, if I get the problem wrong without any justification or without showing my work I might not SEE where I went wrong at all. It is like doing math in my head: so I might have skipped steps while working in my head and cannot figure where I went wrong or I can have incorrect definitions or information. If there is a requirement to write down everything then if the answer is wrong we can pinpoint where any mistakes lie. That is, if we do not justify each and every step how do we know the presenter did not make a mistake? Aren't proofs about all viewing the proof to SEE WHY and verify it? Can you offer any advice to the kind of thinking that I am expressing?

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Do you think a formal proof means anything beyond being a string of symbols in a board game we made up?

strangeWaters